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Integer Sequences
The symbolic character of Mathematica makes possible a uniquely coherent approach to integer sequences, integrating functional forms, equations, generating functions, and explicit lists of values. Powerful new algorithms developed at Wolfram Research make possible recognition of functional forms for an extremely wide range of classes of integer sequences.
Sequence Generation
Table generate a sequence from a formula
RecurrenceTable generate a sequence from a recurrence or functional equation
LinearRecurrence generate a linear recurrence sequence
Sequence Recognition
FindLinearRecurrence find if possible a linear recurrence for a sequence
FindSequenceFunction find general functional forms for integer sequences
Generating Functions
FindGeneratingFunction find generating functions for integer sequences
Fibonacci, LucasL Fibonacci and Lucas numbers and polynomials
BernoulliB  ▪ Factorial  ▪ Binomial  ▪ BellB  ▪ CatalanNumber
DifferenceRoot general representation of solutions to linear difference equations